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Geodetic Set on Graphs of Constant Pathwidth and Feedback Vertex Set Number

Author Prafullkumar Tale

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Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Geodetic Sets
  • NP-hardness
  • Constant Treewidth

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Abstract

In the Geodetic Set problem, the input consists of a graph G and a positive integer k. The goal is to determine whether there exists a subset S of vertices of size k such that every vertex in the graph is included in a shortest path between two vertices in S. Kellerhals and Koana [IPEC 2020; J. Graph Algorithms Appl 2022] proved that the problem is W[1]-hard when parameterized by the pathwidth or the feedback vertex set number of the input graph. They posed the question of whether the problem admits an XP-algorithm when parameterized by the combination of these two parameters. We answer this in the negative by proving that the problem remains NP-hard even on graphs of constant pathwidth and feedback vertex set number.

Cite As Get BibTex

Prafullkumar Tale. Geodetic Set on Graphs of Constant Pathwidth and Feedback Vertex Set Number. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 28:1-28:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.IPEC.2025.28

Author Details

Prafullkumar Tale
  • Indian Institute of Science Education and Research Pune, India

Funding

Research supported by INSPIRE Faculty Fellowship offered by Department of Science and Technology, Government of India.

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